Question: Solve for $x$ and $y$ using elimination. ${-5x+y = 4}$ ${-4x-y = -13}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $-9x = -9$ $\dfrac{-9x}{{-9}} = \dfrac{-9}{{-9}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {-5x+y = 4}\thinspace$ to find $y$ ${-5}{(1)}{ + y = 4}$ $-5+y = 4$ $-5{+5} + y = 4{+5}$ ${y = 9}$ You can also plug ${x = 1}$ into $\thinspace {-4x-y = -13}\thinspace$ and get the same answer for $y$ : ${-4}{(1)}{ - y = -13}$ ${y = 9}$